END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

Going back to one of my oldest creations, I discovered today that it produces some nice Julia set images.

The formula is as follows:

  if (z*z>x*x) {d=z;z=x;x=d;}
  if (y*y>x*x) {d=y;y=x;x=d;}
  if (z*z>y*y) {d=z;z=y;y=d;}

 <standard quaternion (no 4th dimension term)>

 x=x+a;y=y+b;z=z+c; where (a,b,c) is a constant seed value.

Maybe i implemented it wrong, is there the "y,z = 0 must have" issue for the julias again?
For x variants it worked so far:

WOW, beautiful Jesse!!

Very viral 

Jesse: Good ones. b and c can be non-zero. You'll still get discontinuities but also some good variations. I dial up the iterations which tends to hide the discontinuities, but makes the objects more difficult to render.

That is a very good hint Msltoe, thanks!  Increasing the minimum iteration count removes the spread pixels mostly.
The alternative way would be a double check feature in the DE, but in the 4 point method i would have to add 3 whole iterations, what  slows it to much down.

Another variation on the formula: a maximum clip on the Z value can also give some nice structures.

very stylized frog but definitely a great one

As Jesse alluded to in his z-plane cutoff comment, more secrets lie in the interior of these xyz rocks:

Whoah. We need to view these in 4 dimensions, so that we can see all of the interior as well.